# [seqfan] Re: The last digit "d" of a(n) is present in a(n+1+d) --END

David Wilson davidwwilson at comcast.net
Tue Feb 3 02:04:24 CET 2009

I usually like to stay away from "candy sequences" (pleasant to taste but
bad for you in excess), however,

a(1) = 0
a(n+1) = smallest unseen square number sharing no digit with a(n).

Is this sequence finite?

----- Original Message -----
From: "Eric Angelini" <Eric.Angelini at kntv.be>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Sent: Wednesday, January 28, 2009 9:15 AM
Subject: [seqfan] Re: The last digit "d" of a(n) is present in
a(n+1+d) --END

Duncan Booth has computed the seq (see pgm and table
on rec.puzzles or below):

> 1, 2, 10, 20, 102, 103, 104, 112, 113, 123, 124, 134, 135, 136, 137, 140,
> 204, 205, 215, 216, 226, 234, 237, 245, 250, 260, 406, 416, 417, 425, 427,
> 428, 429, 436, 446, 450, 470, 480, 507, 508, 568, 569, 579, 580, 590, 600,
> 607, 608, 618, 628, 629, 639, 649, 650, 670, 680, 708, 718, 728, 729, 739,
> 749, 759, 760, 770, 780, 800, 801, 802, 819, 829, 892, 893, 894, 902, 903,
> 913, 920, 940, 1039, 1093, 1094, 1095, 1096, 1103, 1104, 1114, 1115, 1135,
> 1139, 1146, 1147, 1148, 1150, 1205, 1206, 1207, 1216, 1217, 1279, ...

I'll submit the seq. to the OEIS in a couple of days.
Best,
(and thanks to all)
É.

---

from itertools import islice
def isok(s, needs):
s = str(s)
for c in needs:
if c not in s:
return False
return True
def genS():
required = {}
n = 1
S = 1
while 1:
obdigits = required.pop(n, "")
while not isok(S, obdigits):
S += 1
yield n,S, obdigits
d = S % 10
constrain = n+d+1
d = str(d)
if constrain in required:
required[constrain] += d
else:
required[constrain] = d
n += 1
S += 1
if __name__=='__main__':
sequence = genS()
for n,S,ob in islice(sequence, 100):
print n,S,ob
--------------------------
1 1
2 2
3 10 1
4 20 0
5 102 20
6 103
7 104
8 112 2
9 113
10 123 3
11 124 2
12 134 4
13 135 3
14 136 3
15 137
16 140 4
17 204 40
18 205
19 215 5
20 216
21 226 6
22 234 4
23 237 7
24 245 5
25 250 5
26 260 0
27 406 640
28 416 6
29 417
30 425 5
31 427 7
32 428
33 429
34 436 6
35 446 6
36 450 5
37 470 70
38 480 0
39 507 70
40 508
41 568 86
42 569 6
43 579 9
44 580
45 590 0
46 600 0
47 607 70
48 608
49 618 8
50 628 8
51 629
52 639 9
53 649 9
54 650
55 670 70
56 680 0
57 708 80
58 718 8
59 728 8
60 729
61 739 9
62 749 9
63 759 9
64 760
65 770 0
66 780 80
67 800 80
68 801 80
69 802
70 819 91
71 829 9
72 892 92
73 893 9
74 894
75 902 2
76 903
77 913 3
78 920 2
79 940 40
80 1039 930
81 1093 93
82 1094
83 1095
84 1096
85 1103 3
86 1104
87 1114 4
88 1115
89 1135 53
90 1139 9
91 1146 64
92 1147 4
93 1148
94 1150 5
95 1205 50
96 1206
97 1207
98 1216 6
99 1217
100 1279 97
...

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